The present invention relates to a technique for controlling the size of an image formed by using a template. More particularly, the present invention relates to a sub-grid biasing technique for fabricating photomasks used in VLSI lithography for semiconductor processing, where the photomask has a halftone type pattern so that images formed on semiconductor wafers are related, but not identical, to the sizes and shapes of the photomask features.
Photomask manufacturers continue to be challenged by the demands of customers who require smaller and more precise features on wafers. In particular, the need for subtle differences in line width on features in the same reticle is forcing the use of smaller pixel sizes on raster scan e-beam systems to write customer patterns on a photomask.
A smaller pixel size is beneficial when performing, for example, optical proximity correction of line width biasing. On the logic gate level, for instance, optical proximity effects cause lines situated in different environments, which nominally are of the same dimension, to print differently. This problem may be overcome by biasing the mask features as a function of pitch.
The efficiency of this approach is limited by the pixel size or design grid xcex94. In general, when an image is printed using a template, the width of a line in the template is limited to integral multiples of xcex94. To ensure that an error in the printed image is no larger than xcex94/2 requires a design grid of xcex94. In the case of photomasks used for printing on wafers, the design grid is forced to be smaller still as the wafer critical dimension (CD) becomes increasingly sensitive to mask dimension error (expressed as the mask error factor MEF) at small k1 factors (k1 being CD divided by xcex/NA, where xcex is the wavelength of the light and NA is the numerical aperture of a corresponding exposure system). A xcex94/2 error bound requires a design grid of xcex94/MEF.
For example, if an error bound xcex94/2 of 2.5 nm is desired (which typically will be required in the near future), and the MEF is 2, the required design grid xcex94 on the mask is then 2.5 nm. However, the use of a smaller design grid (smaller pixel size) increases the time required to write a pattern on the mask, which in turn reduces throughput and increases production costs. As shown in FIG. 1, the writing time for a mask of a given size increases quadratically with decreasing design grid size. Although state-of-the-art mask writers allow a design grid xcex94 of 2.5 nm at 1xc3x97reduction, a 6 inch square reticle with such a design grid would require a prohibitively long 30 hours of write time. A design grid of 2.5 nm is thus too small for efficient mask writing.
Accordingly, it is desirable to design with a grid much larger than 2.5 nm (for example, xcex94=25 nm for which the write time is approximately one hour), but still achieve image size increments of 2.5 nm. It will be increasingly important to have this capability when designing future generations of electronic circuits.
A conventional technique for solving this problem is called halftone biasing. The halftone biasing technique incorporates the application of a sub-resolution halftone screen to the edges of features.
FIGS. 2A-2C illustrate the conventional halftone biasing technique. In FIG. 2A, a mask has a shape 20 formed therein of width W. Since the mask is written with a design grid xcex94, width W must be an integral multiple of the design grid xcex94, so that W=nxcex94 where n is an integer. Suppose, however, that a critical dimension of Wxe2x80x2=W+xcex94/2 is desired; that is, the printed image 21 is desired to have a width of Wxe2x80x2 (see FIG. 2B). The halftone biasing technique can be used to achieve this effect. As shown in FIG. 2C, an array of protrusions 22 of width xcex94 is formed on the edge of the mask feature of width W. These protrusions (or xe2x80x9cteethxe2x80x9d on the edge of the feature) have a tight enough segmentation period or pitch, P, so that their details are not resolved when the line is imaged (for example, printed on a semiconductor wafer). However, the presence of these protrusions on the mask influences the width of the printed image. The amount of this influence is determined by the xe2x80x9chalftone percentagexe2x80x9d of the arrangement of the teeth.
This approach is analogous to halftone printing. Since the exposure system acts as a low-pass filter, spatial periods less than xcex/NA(1+"sgr") are not resolved ("sgr" being the partial coherence factor). For mask features having periods beyond this resolution limit, only the average transmittance is captured by the exposure system.
For example, as shown in FIG. 2C, protrusions 22 have a width of one design grid xcex94 and a length D (distance along the edge of the feature) of one design grid xcex94; these protrusions are placed on the edges of the feature 20 with a segmentation period or pitch P=4xcex94. The halftone percentage, per edge of the feature, is defined by (D/P)xc3x97100 (%). Although the protrusions are evident on the mask pattern, they are not replicated in the printed image. Instead, the printed image 23 has straight edges with a critical dimension dependent on the halftone percentage. In this example, with D=xcex94 and P=4xcex94, the halftone percentage is (1/4)xc3x97100%=25%. Each edge of the printed image is thus shifted by xcex94/4. The critical dimension of the feature, when actually printed, is thus Wxe2x80x2=W+2xc3x97(xcex94/4), or Wxe2x80x2=W+xcex94/2. The halftone biasing technique thus permits finer control of the printed image without reducing the design grid (or in e-beam mask generation, the address unit size).
In general, an edge may be biased with an increment of xcex94/n if the edge is segmented into periodic units of nxcex94, where n is a positive integer. (Accordingly, xcex94/n is termed the apparent grid.) However, the increment cannot be made arbitrarily small, because the segmentation period nxcex94 is limited by the resolution of the exposure system; that is, n has a maximum value nmax, given by
nmaxxcex94xe2x89xa6xcex/NA(1+"sgr").
For an exposure system where xcex=248 nm, NA=0.68, "sgr"=0.8 and xcex94=25 nm, this expression yields nmax=8. In such an exposure system, an edge of a feature line 31 designed with a grid of xcex94 can be biased in increments of xcex94/8, if the edge is segmented into periodic units of 8xcex94 as shown in FIG. 3; the printed line 32 then will have a width Wxe2x80x2=W+2xc3x97(xcex94/8)=W+xcex94/4.
There is a need for a sub-grid biasing method which can further reduce the available biasing increment (that is, further reduce the apparent grid relative to the design grid), thereby permitting improved control of the printed feature size while limiting the required writing time for the photomask.
The present invention provides a technique, based on concepts of halftone printing, for controlling feature dimensions in a printed image at very small increments. The invention permits these increments to be smaller than the smallest addressable unit of the template used to produce that image. Specifically, this technique permits fabrication of photomasks yielding images with sizes differing from a nominal width by increments which are small fractions of the minimum template size or pixel size. Stated another way, the present invention provides a technique for reducing the ratio of the apparent grid to the design grid, without decreasing the size of the design grid.
According to a first aspect of the present invention, a template for forming an image includes a feature having one or more edges, with a first array of shapes and a second array of shapes disposed on the edges. The first and second arrays have a first and a second segmentation period, respectively, and the first and second segmentation periods are different. In a typical arrangement, the feature is a line having two edges, and an array of protrusions or indentations is disposed on each edge. Each array may be formed of a plurality of identical shapes repeating at every corresponding segmentation period, each shape having a predetermined length and a predetermined width. Typically, all shapes have an identical width.
A shape in an array may have a length which is a first multiple of the identical width, and a segmentation period of the array which is a second multiple of the identical width, the second multiple being greater than the first multiple.
According to another aspect of the invention, the shapes of the first array and the shapes of the second array have different lengths, in addition to the two arrays having different segmentation periods. Accordingly, a line feature on a template will appear asymmetric with respect to both the length and period of the shapes (protrusions or indentations) along the edges of the feature.
According to another aspect of the invention, at least one edge of the feature has a plurality of arrays of shapes disposed along the edge. Each of the arrays has an inner boundary and an outer boundary with respect to the edge, so that the inner boundary of a given array is coincident with the outer boundary of a neighboring array closer to the edge; the arrays also have different segmentation periods.
According to a further aspect of the invention, a template for forming an image includes a two-dimensional feature having one or more edges, with a first array and a second array disposed on the edges; the arrays have a first segmentation period and a second segmentation period, respectively, with the first and second segmentation periods being different from each other. The feature may be a rectangle having two pairs of opposite edges, with an array of shapes (protrusions or indentations) disposed along each edge. Each array in a pair of arrays on opposite edges has a different segmentation period, for both length and width control of the image.
According to another aspect of the invention, an optical proximity correction process for correcting errors in an image is provided. The process includes the steps of determining an amount by which a width of the image is to be modified, providing a template for producing the image where the template has a feature with edges and arrays as described above, and adjusting the segmentation periods of the arrays to control the width of the image.